Electronic states at vicinal surfaces

Abstract

Vicinal noble metal surfaces with regular arrays of steps and terraces are very convenient model systems to test the electronic properties of lateral nanostructures. Using angle-resolved photoemission with synchrotron radiation we thoroughly characterize electronic states and wavefunctions in a variety of vicinal Cu(111) and Au(111) surfaces. By tuning the terrace width, we can observe the fundamental transition from arrays of non-interacting nano-objects (terraces), where electron states are confined, to lateral coupling between terraces, which leads to superlattice states.

One-dimensional versus two-dimensional electronic states in vicinal surfaces

“…The umklapp bands reveal electron scattering at step edges. In order to estimate the strength of the step barrier, one can conveniently fit the surface band using a periodic 1D Kronig-Penney (KP) potential model [11]. The latter takes its simplest form by assuming a periodic array of δ-function potentials with barrier strength U 0 b, thereby leading to the following dispersion relation:…”

“…However, we observe a relatively strong parabolic background that obscures the QW peaks in the image plot on top of figure 3(b). The background can be minimized by taking the second derivative of the intensity, as shown in the corresponding image plot at the bottom of figure 3(b) [11]. The nature of this dispersing background, which appears repeatedly in vicinal crystals in the QW regime, has been explained recently as being due to the averaging effect on a surface with significant terrace width distribution (TWD) broadening [13].…”

“…In reality, the 1D or 2D nature appears unambiguously defined in surfaces with very large or very small d values, respectively. A less clear behaviour is found for intermediate d values [4,5], [11]- [14]. A number of different explanations have been given to explain this 1D-2D transition, and all of them lead to similar critical values around d c ∼ 20 Å for both Au(1 1 1) and Cu(1 1 1) vicinal surfaces.…”

“…They include the finite coherence length of the surface state [4], the Fermi wavelength of surface electrons [13] and the onset of overlap with bulk states [4,5,7]. The latter is a consequence of the progressive formation of a surface resonance as the projected bulk band gap around the Fermi energy closes [11]. Such surface-state/resonance transition is consistent with STM spectroscopy [14], which nicely reveals the coexistence of mixed 1D-2D components below the Fermi energy in 20-40 Å terraces, as well as with recent theoretical calculations [16].…”

“…In fact, by scanning hν one probes the different surface state Fourier components that fill up the L line (see figure 7). On the other hand, photoelectron interference effects provoked by the step array lead to similar photon energy dependence, such that one cannot separate both effects [11,18].…”